The first four times the Patriots were the first or second seed in the AFC under Belichick, they went to the Super Bowl - 2001 (2), 2003 (1), 2004 (2), and 2007 (1) - with a victory in their first three appearances.

Of course, last season ended the streak. The Patriots were the top seed and rudely bounced at home by the Jets, 28-21.

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Despite compiling a 4-1 record, the Patriots have not come out like gangbusters after a week of rest. They have been rusty and struggled to put away inferior teams until the second half.

In the five playoff games after a bye, the Patriots have trailed twice at halftime, were tied once, led by a touchdown only to be tied in the third quarter, and led by a field goal.

Here’s a breakdown of the struggles:

- 2001: The second-seeded Patriots (11-5) trailed the third-seeded Raiders (10-6) at halftime, 7-0. The Patriots had just four first downs and didn’t convert a third down. Tom Brady had a 32.2 passer rating after two quarters. The Patriots trailed, 13-3, in the third quarter before scoring the final 13 points to win the “Tuck Rule’’ game, 16-13.

- 2003: The top-seeded Patriots (14-2) led the fifth seed Titans (12-4) at halftime, 14-7, but found themselves tied with 4:14 left in the third quarter. Brady completed just 12 of his 23 passes in the first half. The Patriots took the lead on an Adam Vinatieri 46-yard field goal with 4:06 to play after converting a fourth-and-3 at the Tennessee 33-yard line and won, 17-14.

- 2004: The second-seeded Patriots (14-2) led the rival Colts (12-4, third seed) at halftime, 6-3. The teams had very similar stats in the first half except for Corey Dillon’s 68 yards on eight carries, most of which came on a 42-yard run. Brady was sacked twice in the first half. The Patriots won, 20-3, in their most impressive post-bye performance.

- 2007: The 16-0 Patriots watched the fifth-seeded Jaguars (11-5) come into Gillette, take the kickoff, and march 80 yards in nine plays to take a 7-0 lead. The Patriots answered right back, and the teams were eventually tied, 14-14, at halftime. Brady completed all 12 of his passes for 120 yards and a touchdown in the first half. But Jaguars quarterback David Garrard had a higher passer rating (150.6 to 136.1) as he completed 12 of 14 for 149 yards and two touchdowns. The Patriots scored 17 points on their first three possessions of the second half on their way to a 31-20 victory.

- 2010: The top-seeded Patriots (14-2) came out stumbling against the sixth-seeded Jets (11-5), a team New England had just beaten, 45-3, on the same field a month earlier. Brady threw his first interception in 335 attempts on the Patriots’ opening possession, and while the Jets didn’t get any points out of it, it gave them confidence. A drop in the end zone by tight end Alge Crumpler led to a New England field goal on the next possession. The Patriots, who allowed Brady to be sacked five times, would go more than two quarters without scoring again and trailed, 14-3, at halftime. The Jets took a 28-14 lead with 1:41 to play before the Patriots made it 28-21 with 24 seconds remaining.

Aside from struggling in the first half, the common theme to the Patriots’ post-bye games seems to be that, as a veteran team, they were mentally tough, and knew how to grind out games in the second half, especially on defense.

In the first four games, the Patriots allowed a total of 19 points in the second half, and just 3 came in the fourth quarter (’07). In ’01, ’03, and ’04 - years the Patriots went on to win the Super Bowl - they pitched shutouts in the fourth quarter defensively.

That’s a mentally tough veteran group rising up at the most important time.

Against the Jets, the Patriots allowed 14 second-half points - and all of them came in the fourth quarter.

Will things change this time around?

There’s no question that this team has shown much more tenacity and mental toughness than some previous versions. It’s just that they haven’t had to show that against a playoff-caliber team in a victory since hosting the Cowboys Oct. 16.

Against the two playoff-caliber teams after that, the Patriots lost on the road to the Steelers and at home to the Giants.

There’s no question the Patriots have the chops offensively. Brady, Wes Welker, Deion Branch, Matt Light, Logan Mankins, and Kevin Faulk have all been a part of multiple playoff victories.

Defensively, only Vince Wilfork has experienced a postseason victory wearing a Patriots uniform.

The Patriots have brought in players who know what it takes to win in the playoffs. Defensive end Shaun Ellis has won six playoff games and went to the past two AFC Championship games with the Jets, along with safety James Ihedigbo. End Mark Anderson won two and went with the Bears to the Super Bowl in 2006. Linebacker Niko Koutouvides won a wild-card game with the Seahawks in 2004. Gerard Warren won a divisional playoff with the Broncos in 2005. Linebacker Tracy White has won playoff games with the Packers and Eagles.

Maybe those players can fill the gaps that last year’s Patriots were missing.

If history is any judge, the Patriots will not simply run through the playoffs. They will have to grind out every game. Maybe a tweak to the practice routine would help. Or maybe it will just have to come from within.

HOMECOMING GAME

Bicknell back in town as a Buffalo assistant

Holliston native and former Boston College tight end Bob Bicknell will be roaming the Gillette Stadium sideline today as the second-year tight ends coach for the Bills, and it’s always a special visit.

“Just because it’s home and that’s a team obviously I grew up watching and rooting for in that area,’’ said Bicknell, the 42-year-old son of former BC coach Jack Bicknell, who also will be at the game.

“I grew up in Holliston, lived there for a lot of years. I remember the old Sullivan Stadium when my dad was at Boston College and some of those big games they had, Penn State and Alabama. I remember being on those sidelines.

“So obviously it’s a special place and it’s always exciting to go back.’’

Bicknell touched on a variety of topics in a conversation last week.

On the progress of the Bills: “We started out, obviously, very well [3-0], and things were going great, and this league is just a tough league. Then you have some games that you have a chance to win that you don’t win, and then you have a couple games where you didn’t play great and before you know it, you’ve lost a few in a row.

“But I think the second year you’re in a program, we’re really not that far away, and I think that’s the good part about it. We’re a couple games away from being able to play for the playoffs. I think that’s a process you go through. I do think we’re on the right track.’’

On the progress of Bills tight end Scott Chandler, who has gone from one catch his first four seasons with four teams to 35 catches for 360 yards and six touchdowns this season: “Scott has bounced around in this league and sometimes you’re not in the right situation, but he’s got a lot of talent, he’s made some great plays for us. We were lucky to get him.’’

On Bills tight end Lee Smith, a fifth-round pick of the Patriots who was waived in final cuts and is now on injured reserve: “Lee is as good as I’ve been around in this league as a true blocking tight end. Sometimes guys fit in certain situations that you need and they don’t fit in others. I think for us, he’s a blocking tight end. He was a great addition. I know New England really liked him too.’’

On Patriots guard Brian Waters, whom he coached in Kansas City: “If you just put up a picture of what a pro is, a guy that obviously is very talented, he’s extremely strong and all those things. But he’s got an unbelievable ability to prepare, to fit into a system, he’s just a great player. He’s a Hall of Famer, a perennial Pro Bowler, who can play as long as he wants and he’ll be successful. I think the best compliment you can give Brian Waters is just to say he’s a true pro.’’

On Patriots tight end Rob Gronkowski: “He’s awesome. He’s the best, in my opinion, combination tight end. He’s it. He can block and do the other things. We all liked him out of college, and what an unbelievable pick for New England. I was around Tony Gonzalez, and he is awesome. There’s a few of those guys, and that’s the type of future I think he’ll have if he stays healthy. I’ve just watched him as a fan. He does a lot of things well for them and they do an unbelievable job of devising plans for those guys.’’

BRUTALLY HONEST

Jones-Drew tackles issue of concussions

Interesting perspective from Jaguars running back Maurice Jones-Drew on concussions in the league.

“I’ve had concussions before, and it wasn’t this big deal about concussions,’’ he said. “The only reason they’re making a big deal about concussions right now is because the league is getting sued over it. Before this, you never heard about it. A couple of years ago, you didn’t hear anything about it.’’

At least eight lawsuits have been filed in the past year against the NFL by dozens of retired players who say they have medical problems related to brain injuries from their time in professional football.

“You know playing football you’re going to get hurt, right?’’ Jones-Drew said. “In the back of your mind, you’ve got to know that the worst that can happen is you can break your neck and be paralyzed for the rest of your life, right?

“You have to go into every game knowing that could be what happens. Any given play, that could happen to you, right? So there it is. When you sign these deals, you know in the back of your mind, that’s what can happen.’’

Jones-Drew also feels that players will continue to hide concussions from teams, because if a player is deemed to have a history of them, other teams will be hesitant to sign him.

“I would do anything for my kids,’’ Jones-Drew said. “If they’re happy, I’m happy. I think they would appreciate it. As long as my kids would be happy with what I did, that’s what this life is about: sacrifice. It’s not about you anymore, you know?’’

BLASTING OFF

Pereira makes a ruling on Gruden: ‘blowhard’

Mike Pereira, who was the NFL’s vice president for officiating from 2004-09 before taking an analyst role with Fox, really let former coach Jon Gruden have it for his comments during the Monday night game between the Saints and Falcons.

“I am not a fan of Gruden’s,’’ Pereira wrote at foxsports.com. “Not today, not yesterday, not when I worked for the NFL and not when I was working on the field as a side judge. He was a loudmouth as a coach who constantly disrespected officials and he is a blowhard in the broadcast booth who spouts off when he doesn’t know what he is talking about.

“I respect his knowledge about the X’s and O’s when it comes to coaching and playing the game of football, but I have very little respect for him when it comes to officiating and his knowledge of the rules.’’

“To me, the second you agree to step into the broadcast booth, you agree to learn the rules,’’ Pereira wrote. “It goes with the job. You, as an announcer, have an obligation to know the rules. You are free to pontificate as to whether or not you like a rule, but you must present the rule first.’’

ETC.

Nickel package

1. Very nice gesture by the Patriots players to have a painting commissioned for owner Robert Kraft in memory of his late wife, Myra. There has certainly been an angel looking over this team this season.

2. Rex Ryan said Peyton Manning as a free agent wouldn’t be a consideration for the Jets. Two words: Yeah. Right. Of course they would run to Manning. And they should.

3. Ryan does need to do something about offensive coordinator Brian Schottenheimer. He should return, but 59 pass attempts against the Giants is just ridiculous.

4. Hope you find happiness in retirement, Jason Taylor. Nick Saban said that if Taylor played in a 3-4 his entire career, he would be a Hall of Famer. Bill Belichick has echoed those thoughts and tried to sign Taylor before the 2010 season. Taylor will retire sixth on the all-time list of sacks; he has 139.5 heading into his final game.

5. Farewell, Houston Antwine. The man was just a force for the Boston Patriots.

By the numbers

11.5: Sacks that Taylor had against Tom Brady in his career, his most of any quarterback. Drew Bledsoe (6.5) was next on Taylor’s hit list.

44: Passes of 25 yards or more allowed by the Patriots this season, tied for second all-time with the 2004 Chiefs. The 1999 49ers lead with 48.

82: Gross passing yards the Patriots need to allow against the Bills to have the worst pass defense in NFL history. The Patriots are at 4,670 gross passing yards. The 1995 Falcons lead with 4,751.

135: Net passing yards needed for the Patriots to set the record for most allowed in a season. The 1995 Falcons lead with 4,541. The Patriots are at 4,407.

Short yardage

With a 128-yard lead over LeSean McCoy of the Eagles, Maurice Jones-Drew of the Jaguars has virtually wrapped up the NFL rushing title. But he said it would be more of an honor to top former Patriot Fred Taylor’s team record of 1,572. Jones-Drew is at 1,437. “I think that would be more special,’’ Jones-Drew said. “This guy taught me how to play the game, showed me the way in the NFL, how to be a player and how to be consistent. And in this league, that’s what it is all about, is consistency.’’ . . . Chiefs quarterback Kyle Orton isn’t saying much about his opportunity to knock the Broncos - the team that cut him in favor of Tim Tebow - out of the playoff picture with a victory today. “The only guys I’m trying to prove something to are my teammates,’’ Orton said. “I really don’t worry about anything else. You’ve got to worry about yourself. There’s so much you’ve got to play for every week. There’s still plenty to play for just for your 53 [players]. That’s the approach you’ve got to take.’’ . . . Texans defensive coordinator Wade Phillips expects to work from the press box after missing two games following kidney and gallbladder surgery . . . Amazing that the Eagles could finish 5-1 against the NFC East with a victory against the Redskins. What a dream . . . This will be the first time (in a full season) that the NFC East winner has fewer than 10 wins since the division was created in 1970. The lone exception was the strike-shortened 1982 season, when teams played nine games and the division champ won eight . . . Want to know why the Redskins continue to struggle? Turnovers. Washington has committed at least one turnover in 29 straight games, the NFL’s longest active streak . . . The Buccaneers are 0-7 since signing Albert Haynesworth. The Patriots are 7-0 since cutting him. We’re just saying. The quarterback differential might have something to do with it as well.